An Introduction to Probability and Statistical Inference, 2nd Edition

Inside Back Matter

Distribution	Moment Generating Function
Binomial, B(n, p)	$M\left(t\right)={\left(p{e}^t+q\right)}^n,\text{?}t\in \Re$
Bernoulli, B(1, p)	$M\left(t\right)=p{e}^t+q,\text{?}t\in \Re$
Geometric	$M\left(t\right)=\frac{p{e}^t}{1-q{e}^t},\text{?}t<-\log \text{?}q$
Poisson, P(λ)	$M\left(t\right)=\exp \text{?}\left(\mathrm{\lambda }{e}^t-\mathrm{\lambda }\right),\text{?}t\in \Re$
Hypergeometric	—
Gamma	$M\left(t\right)=\frac{1}{{\left(1-\beta t\right)}^{\alpha }},\text{?}t<\frac{1}{\beta }$
Negative Exponential ...